Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Vector Algebra: Method of Components

Vector Algebra: Method of Components

It is cumbersome to find the magnitudes of vectors using the parallelogram rule or using the graphical method to perform mathematical operations like addition, subtraction, and multiplication. There are two ways to circumvent this algebraic complexity. One way is to draw the vectors to scale, as in navigation, and read approximate vector lengths and angles (directions) from the graphs. The other way is to use the method of components.
In many applications, the magnitudes and directions of...

Vector Algebra: Graphical Method

Vector Algebra: Graphical Method

Vectors can be multiplied by scalars, added to other vectors, or subtracted from other vectors. The vector sum of two (or more) vectors is called the resultant vector or, for short, the resultant.
We use the laws of geometry to construct resultant vectors, followed by trigonometry to find vector magnitudes and directions. For a geometric construction of the sum of two vectors in a plane, we follow the parallelogram rule. Suppose two vectors are at arbitrary positions. Translate either one of...

Vector or Cross Product

Vector or Cross Product

Vector multiplication of two vectors yields a vector product, with the magnitude equal to the product of the individual vectors multiplied by the sine of the angle between both the vectors and the direction perpendicular to both the individual vectors. As there are always two directions perpendicular to a given plane, one on each side, the direction of the vector product is governed by the right-hand thumb rule.
Consider the cross product of two vectors. Imagine rotating the first vector about...

Magnetic Vector Potential

Magnetic Vector Potential

In electrostatics, the electric field can be written as the negative gradient of the potential. In magnetostatics, the zero divergence of the magnetic field ensures that the magnetic field can be expressed as the curl of a vector potential. This potential is known as the magnetic vector potential.
Consider an ideal solenoid with n turns per unit length and radius R. If I is the current through the solenoid, the magnetic field inside the solenoid is expressed as the product of vacuum...

Acceleration Vectors

Acceleration Vectors

In everyday conversation, accelerating means speeding up. Acceleration is a vector in the same direction as the change in velocity, Δv, therefore the greater the acceleration, the greater the change in velocity over a given time. Since velocity is a vector, it can change in magnitude, direction, or both. Thus acceleration is a change in speed or direction, or both. For example, if a runner traveling at 10 km/h due east slows to a stop, reverses direction, and continues their run at 10 km/h due...

Vector Operations

Vector Operations

Vectors are physical quantities that have both magnitude and direction. The vector operations include addition, subtraction, and scalar multiplication.
A vector multiplied by a scalar value is called scalar multiplication. The result obtained is a new vector with a different magnitude. If the scalar is positive, the direction of the vector remains the same, but if it is negative, the direction of the vector is reversed. For example, the product of the mass and velocity yields the momentum.

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

A benchmarking framework and dataset for learning to defer in human-AI decision-making.

Scientific data·2025

Same author

DALL-M: Context-aware clinical data augmentation with large language models.

Computers in biology and medicine·2025

Same author

Weakly-supervised preclinical tumor localization associated with survival prediction from lung cancer screening Chest X-ray images.

Computerized medical imaging and graphics : the official journal of the Computerized Medical Imaging Society·2024

Same author

A Measure of Synergy Based on Union Information.

Entropy (Basel, Switzerland)·2024

Same author

MDF-Net for abnormality detection by fusing X-rays with clinical data.

Scientific reports·2023

Same author

Orders between Channels and Implications for Partial Information Decomposition.

Entropy (Basel, Switzerland)·2023

Search research articles

Related Experiment Video

Updated: May 16, 2026

Combining Eye-tracking Data with an Analysis of Video Content from Free-viewing a Video of a Walk in an Urban Park Environment

Combining Eye-tracking Data with an Analysis of Video Content from Free-viewing a Video of a Walk in an Urban Park Environment

Published on: May 7, 2019

Activity recognition using a mixture of vector fields.

Jacinto C Nascimento¹, Mário A T Figueiredo, Jorge S Marques

¹Instituto de Sistemas e Robótica, Instituto Superior Técnico, Lisbon, Portugal. jan@isr.ist.utl.pt

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society

|November 30, 2012

Summary

This summary is machine-generated.

This study models diverse pedestrian trajectories in video surveillance using a few typical motion fields and a switching mechanism. The approach effectively classifies movement patterns in complex scenes.

Related Experiment Videos

Last Updated: May 16, 2026

Combining Eye-tracking Data with an Analysis of Video Content from Free-viewing a Video of a Walk in an Urban Park Environment

Combining Eye-tracking Data with an Analysis of Video Content from Free-viewing a Video of a Walk in an Urban Park Environment

Published on: May 7, 2019

Area of Science:

Computer Vision
Artificial Intelligence
Pattern Recognition

Background:

Analysis of moving objects in video is a core computer vision problem.
Pedestrian trajectory analysis is crucial for video surveillance applications.

Purpose of the Study:

To propose a novel method for modeling diverse pedestrian trajectories in video surveillance.
To represent complex motion patterns using a limited set of motion fields and a space-varying switching mechanism.

Main Methods:

Modeling trajectories with a small set of motion/vector fields.
Incorporating a space-varying switching mechanism for dynamic behavior changes.
Utilizing an expectation-maximization algorithm for model parameter learning.

Main Results:

Demonstrated that complex motion patterns can be modeled by a few typical behaviors.
Successfully applied the model to trajectory classification tasks.
Validated the approach using both synthetic and real-world video data.

Conclusions:

The proposed model effectively captures and classifies diverse pedestrian movements in surveillance.
The combination of motion fields and switching mechanisms enhances trajectory analysis.
The expectation-maximization algorithm provides an efficient way to learn model parameters.